Reproducing Type II White-Light Solar Flare Observations withElectron and Proton Beam Simulations

Reid, A., Milligan, R. O., Procházka, O., Simoes, P. J. A., Allred, J. C., & Mathioudakis, M. (2018). ReproducingType II White-Light Solar Flare Observations with Electron and Proton Beam Simulations. The AstrophysicalJournal, 862(76), [76]. https://doi.org/10.3847/1538-4357/aaca37

Published in:The Astrophysical Journal

Document Version:Publisher's PDF, also known as Version of record

Queen's University Belfast - Research Portal:Link to publication record in Queen's University Belfast Research Portal

Publisher rightsCopyright 2018 the authors.This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.

General rightsCopyright for the publications made accessible via the Queen's University Belfast Research Portal is retained by the author(s) and / or othercopyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associatedwith these rights.

Take down policyThe Research Portal is Queen's institutional repository that provides access to Queen's research output. Every effort has been made toensure that content in the Research Portal does not infringe any person's rights, or applicable UK laws. If you discover content in theResearch Portal that you believe breaches copyright or violates any law, please contact openaccess@qub.ac.uk.

Download date:30. Mar. 2021

https://doi.org/10.3847/1538-4357/aaca37https://pure.qub.ac.uk/en/publications/reproducing-type-ii-whitelight-solar-flare-observations-with-electron-and-proton-beam-simulations(05f5f529-bb71-48b9-8fcb-6a53deeba811).html

Reproducing Type II White-light Solar Flare Observations with Electron and ProtonBeam Simulations

Ondrěj Procházka1 , Aaron Reid1 , Ryan O. Milligan1,2,3,4 , Paulo J. A. Simões2 , Joel C. Allred3 , andMihalis Mathioudakis1

1 Astrophysics Research Centre, Queen’s University Belfast, UK; oprochazka01@qub.ac.uk2 SUPA School of Physics and Astronomy, University of Glasgow, UK3 NASA Goddard Space Flight Centre, Greenbelt, MD 20771, USA

4 Department of Physics, Catholic University of America, 620 Michigan Avenue, Northeast, Washington, DC 20064, USAReceived 2018 March 1; revised 2018 May 31; accepted 2018 May 31; published 2018 July 24

Abstract

We investigate the cause of the suppressed Balmer series and the origin of the white-light continuum emission inthe X1.0 class solar flare on 2014 June 11. We use radiative hydrodynamic simulations to model the response ofthe flaring atmosphere to both electron and proton beams, which are energetically constrained using Ramaty HighEnergy Solar Spectroscopic Imager and Fermi observations. A comparison of synthetic spectra with theobservations allows us to narrow the range of beam fluxes and low energy cutoff that may be applicable to thisevent. We conclude that the electron and proton beams that can reproduce the observed spectral features are thosethat have relatively low fluxes and high values for the low energy cutoff. While electron beams shift the upperchromosphere and transition region to greater geometrical heights, proton beams with a similar flux leave theseareas of the atmosphere relatively undisturbed. It is easier for proton beams to penetrate to the deeper layers and notdeposit their energy in the upper chromosphere where the Balmer lines are formed. The relatively weak particlebeams that are applicable to this flare do not cause a significant shift of the τ=1 surface and the observed excessWL emission is optically thin.

Key words: Sun: chromosphere – Sun: flares – Sun: photosphere – Sun: UV radiation – Sun: X-rays, gamma rays

1. Introduction

Despite a large number of white-light flare (WLF) observa-tions, the processes that deliver energy to the deepest layers ofthe Sun’s atmosphere where optical emission is believed to beformed, are poorly understood (Hudson 2016). Watanabe et al.(2010) and Watanabe et al. (2017) reported observations ofWLFs, but were unable to conclude how the required energywas delivered to the deeper layers of the atmosphere. Fletcheret al. (2007a) analyzed WLF observations from the TransitionRegion and Coronal Explorer (TRACE) (Handy et al. 1999)and the Ramaty High Energy Solar Spectroscopic Imager(RHESSI; Lin et al. 2002) of WLFs with classifications rangingfrom C4.8 to M9.1. They estimated that an electron beam witha low energy cutoff below 25 keV could carry sufficientenergy, but concluded that electrons with such low energiescannot penetrate sufficiently deep into the lower solaratmosphere. X-ray spectroscopy of an X1 class flare showedan unusually high low energy cutoff of ≈100 keV, which mayexplain the lack of substantial energy deposition in thechromosphere (Warmuth et al. 2009). Alfvén waves areanother possible mechanism that can explain the rapid energytransport from the corona to the lower solar atmosphere duringthe impulsive phase of flares (Fletcher & Hudson 2008; Kerret al. 2016; Hao et al. 2017; Reep et al. 2018).

The wide range of WLFs that have been observed to date canbe grouped into two main categories. Type I WLFs show thepresence of Balmer and Paschen edges and have more intenseemission, while the events with significantly weaker hydrogen

emission lines and a relatively flat continuum are grouped intoType II (Canfield et al. 1986; Machado et al. 1986).Observations of Type II WLF were first presented by Boyeret al. (1985). Their spectral analysis, which assumed opticallythin emission, ruled out an origin of the WL emission as aresult of the Paschen continuum. Optically thin H− emissionwould imply intense heating of the lower atmosphere butrequires a process that would deposit significant amounts ofenergy in the deeper layers. Their calculations have shown thatthis deposition of energy would be accompanied with anincrease in temperature by ≈2000 K at a height of ≈200 kmabove the photospheric floor or an increase in temperature by≈150 K over the entire photosphere and chromosphere. Basedon observations of three WLFs, Fang & Ding (1995) concludedthat besides the observed spectral differences, a temporalmismatch between the WL and HXR emission is also anindication of Type II WLFs. Potts et al. (2010) associated thetemporal and spatial correspondence of WL emission and hardX-ray sources with the so-called thick-target model. Assumingthat the WL excess emission originated above the photosphere,their analysis of an X3-class flare concluded that the WL excessemission was optically thin.Some of the scenarios used to explain Type II WLFs include

photospheric reconnection, radiative back-warming, and particlebeams that are able to penetrate through the chromosphere.Photospheric reconnection would be most efficient at thetemperature minimum region (TMR) and result in localizedheating in the photosphere (Li et al. 1997, Chen et al. 2001 andLitvinenko 1999). Ding et al. (1999) modeled the flarecontinuum emission using a high-energy particle beam acceler-ated in the TMR. This led to an initial decline in intensity (so-called black-light flare), absence of the Balmer discontinuity, andonly a minor disturbance in the chromosphere where the Balmer

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 https://doi.org/10.3847/1538-4357/aaca37© 2018. The American Astronomical Society. All rights reserved.

Original content from this work may be used under the termsof the Creative Commons Attribution 3.0 licence. Any further

distribution of this work must maintain attribution to the author(s) and the titleof the work, journal citation and DOI.

1

https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296mailto:oprochazka01@qub.ac.ukhttps://doi.org/10.3847/1538-4357/aaca37http://crossmark.crossref.org/dialog/?doi=10.3847/1538-4357/aaca37&domain=pdf&date_stamp=2018-07-24http://crossmark.crossref.org/dialog/?doi=10.3847/1538-4357/aaca37&domain=pdf&date_stamp=2018-07-24http://creativecommons.org/licenses/by/3.0

lines are formed. Machado et al. (1989) estimated that electronswould require an energy of at least 170 keV to reach the TMR,meanwhile protons would need energies of 6MeV. Theyconcluded that the electron energy is too high and given thelack of observational evidence for protons the particles must bestopped in the chromosphere where the Balmer continuum isformed. Balmer continuum radiation (through the process of back-warming) could provide the energy for heating the photosphereleading to H− emission and a WL continuum. Allred et al. (2005)used more sophisticated chromospheric heating models and foundthat back-warming contributes only 10% to the heating. In arecent study, Simões et al. (2017) used RADYN simulations todetermine the formation of the infrared continuum in flares andfound no enhancement in the photospheric blackbody emission.

The scenario of flare energy transfer by proton beams was firstproposed by Švestka (1970), who calculated a threshold of20MeV as the lowest energy required by protons to penetrate intothe upper photosphere. Simnett (1986) highlighted that thetraditional flaring scenario that employs electron beams with alow energy cutoff of 20–25 keV is not consistent with manyobservations and favored shock accelerated protons to explain thethermal X-ray bursts at the beginning of the impulsive phase.More recent observations by Martínez Oliveros et al. (2012) foundboth WL and HXR sources in the photosphere during theimpulsive phase of a flare. However, these observations cannot beexplained with any plausible electron beam scenario because20–25 keV electrons cannot penetrate to heights of ≈195 kmabove the photospheric floor. In recent years, RHESSI has beenused to obtain electron beam parameters that are then used asinput into radiative hydrodynamic simulations. The compressionof the lower atmosphere, as a result of the electron beam heating,allows for higher energy electrons to penetrate to lower altitudes.The location of the deepest penetration coincides with the peak inthe contribution function of the Balmer continuum (Kennedyet al. 2015).

Procházka et al. (2017) reported the observation of an X1WLF that was observed at the Ondrějov Observatory, CzechRepublic, with the Image Selector (IS, Kotrč et al. 2016)instrument, providing rare optical spectra (spectral resolution∼0.03 nm per pixel) in conjunction with modern space-basedinstruments. The authors reported no emission in the higher orderBalmer lines, as well as weak emission in Lyman lines andLyman continuum (LyC). They compared these observationswith synthetic line profiles generated by two distinct heatingmodels: one using a generic electron beam, and one where theheating was deposited directly into the TMR. The deposition ofenergy in the TMR led to an increased optical continuum andonly weak emission in the wings of the Balmer lines and theBalmer jump, in broad agreement with the observations. Thecontinuum generated by the model included contributions fromboth blackbody emission and Balmer continuum. Their analysisconcluded that depositing the energy deep in the atmosphere canlead to increased continuum and a suppression of the hydrogenline emission. Although electron beams cannot be excluded fromthe interpretation of the observations, the parameters of the beammust be rather extreme.

In this paper, we carry out a more detailed analysis ofelectron and proton beam heating models in order to explainthe observations of the type II WLF presented by Procházkaet al. (2017). In Section 2, we provide an outline of the data setsobtained from both ground- and space-based instruments. InSection 3, we model the response of the lower solar atmosphere

to both electron and proton beams using 1D radiativehydrodynamics. In Section 4, we present our findings, with adiscussion presented in Section 5. The conclusions aresummarized in Section 6.

2. The X1 Flare on 2014 June 11: Observations and DataAnalysis

On 2014 June 11, an X1.0 WLF (that peaked at 09:06 UT) inactive region NOAA 12087 (location S18E57) was observedby the IS instrument, which provides high-temporal resolutionspectroscopy (10 spectra per second) in the λ=350–485 nmwavelength range, as well as Hα context images. The ISspectra are integrated over an area of ∼1 arcmin in diameter.Using the Hα images, we estimate the flaring kernels to cover7% of this area, indicating a small filling factor of ff=0.07.Due to the nature of the observations, the noise may mask anyweak Balmer line emission. We quantify these effects in thespectrum of Figure 1 by measuring the height of the Ca II K line(from the continuum) with respect to the flux at the expectedlocation of Hγ. Based on this analysis, we conclude that the Hγversus Ca II K line ratio must be lower than 0.1. Errors in ourmeasurements reached 0.5% for wavelengths ∼440 nm andintegration times of 30ms and up to 2% for the Ca II K and Hlines and wavelengths of ∼360 nm. The errors were determinedas the standard deviation over a set of 50 reference spectra. Theobservations in the visible range showed that the higher Balmerlines remained in absorption while the Hα intensity showed aclear increase during the flare (Figure1 in Procházkaet al. 2017). The higher order Balmer lines (e.g., Hγ) do notshow the characteristically strong emission that may beexpected during the impulsive phase. Any systematic rise bothredward and blueward of the Balmer jump was not detectedduring the impulsive phase (Figure 1(e)). It should be notedthat the IS spectrum shown in Figure 1(e) is different fromthose presented in Procházka et al. (2017), as, in this work, thereference preflare spectrum was taken much closer to the flareonset (08:54:45–08:55:15 UT). Observations by the EUVSensor on Geostationary Operational Environmental Satellite(GOES/EUVS; Viereck et al. 2007) and the SDO/EUVVariability experiment (SDO/EVE; Woods et al. 2012) showeda similar behavior in the Lyman series, with weak emission inthe Lyα line (Figure 1(b)) and LyC (Figure 1(c)), respectively.

2.1. White Light from SDO/HMI Observations

The WL continuum emission near the Fe I 617.3 nm linerecorded by the Helioseismic and Magnetic Imager (SDO/HMI, Scherrer et al. 2012) peaked at the same time and wascospatial with the hard X-ray source (Figures 1(a) and (d); seealso Figure2 in Procházka et al. 2017). We were only able toreliably determine a lower limit of the WL contrast in theobservations due the large temporal and spatial variations in theactive region (Figure 1(a)). For the northern and southernkernels, the WL contrast was 1.07 and 1.05 respectively.We used HMI continuum images to estimate the area of theWL emission. We applied intensity thresholding on differenceimages. This allowed us to select upper and lower limits of theflaring area. If we consider the location of the flare (S18E57),the geometric distortion would cause the observed flaring areato look about 2.5 times smaller. The resulting area was in arange of 1.1×1017–3.3×1017 cm2. This area, combined withthe power of the nonthermal electrons (Section 2.2), provided

2

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

lower and upper estimates on the energy flux for both theelectron and proton beams.

2.2. Hard X-Rays from RHESSI Observations

RHESSI observed the flare in the time interval 8:18 UT to9:21UT. The RHESSI light curve shows that the higher energybands peaked at 9:04:45UT. X-ray spectra were generated forten 12 s intervals across the flare peak using only detector #7(Figure 2). At this stage of the mission, the detectors hadsuffered severe degradation and detector #7 was found to havethe highest sensitivity out of the nine collimators. Note that theRHESSI detectors were annealled for the fourth time between2014 June 26 and 2014 August 13; just 15 days after this flareoccurred.

Initial attempts to fit the RHESSI spectra with a combinationof a multithermal component at lower energies and anonthermal component at higher energies, (as well as thestandard albedo, pulse-pile up, and detector response matrixcorrections), failed to provide consistent estimates for the lowenergy cutoff (EC). Ordinarily, hard nonthermal spectra areoften easier to fit than softer spectra as the nonthermal tail

deviates more significantly from the thermal Maxwelliandistribution. However, as this flare exhibited an unusuallyhard slope (δ∼3), the flattening of the photon spectrum belowEC was similar to the slope above EC making it difficult todistinguish between different values of EC. To this end, thefitting process was performed with fixed values of EC at 20, 40,60, 80, 100, and 120 keV, while the slope and normalizationfactor (i.e., the number of electrons) were allowed to vary. Thequality of the fit, represented with χ2, turned out to beindependent of the value of EC (Figure 2).The value of EC is crucial for calculating the total power of

nonthermal electrons, because we assume that the electrondistribution above EC is given by a power-law function;meanwhile, it is equal to zero below this value (Holmanet al. 2011). For a fixed amount of energy in nonthermalelectrons, a low value of EC leads to a high power innonthermal electrons above EC and vice versa. Having obtainedthe power in nonthermal electrons from the fits to the RHESSIspectra for each EC, the flux (in erg cm

−2 s−1) was found bydividing by the WL area derived from HMI data (Table 1), asdescribed in Section 2.1.

Figure 1. Summary of observations taken during the 2014 June 11 flare. (a) Lightcurves of WL emission from the northern (red) and southern (blue) footpoints ashighlighted in panel (d). GOES 1–8 Å time profile is also shown for reference. (b) Lyα light curve from GOES/EUVS. (c) LyC light curve from SDO/EVE. Thevertical dashed and dotted lines in panels (a)–(c) denote the times of the WL image (in panel d) and IS spectrum (in panel e), respectively. (d) SDO/HMI WL imageshowing the location of two WL kernels. (e) IS flare excess spectrum relative to a preflare profile (averaged over 09:04:45–09:05:15 UT). The reference spectrum wasrecorded at 08:54:45–08:55:15UT.

3

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

2.3. Gamma-Rays from Fermi/GBM Observations

The Gamma Ray Burst Monitor (GBM) on board the FermiGamma-ray Space Telescope (Meegan et al. 2009) detectedsufficient counts in the 200–10,000 keV range to allow anestimate of the parameters of the accelerated protons. Thebackground counts were determined by using a linear fit to thecounts before (between 08:56:08 and 09:01:20 UT), and after(09:08:39 and 09:21:47 UT) the flare. After subtracting thebackground, the bismuth germanite detector (BGO) countswere integrated between 09:04:13 and 09:05:35UT to producethe spectrum. The spectrum was fitted with a power law tocapture the electron bremsstrahlung component, Gaussians forthe 511 keV electron–positron annihilation line and 2.223MeV

neutron capture lines, and a template to describe the narrow de-excitation nuclear lines (Figure 3). The template for nuclearlines is included as standard in OSPEX (Schwartz et al. 2002),and it is calculated for a flare at a heliocentric angle of 60° byassuming a downward isotropic distribution of ions and apower-law energy distribution with spectral index 4 and an α/pratio of 0.22. The template is normalized so that a value of1 photon s−1 cm−2 keV−1 corresponds to 8.5946×1029 protonsper second with energies above 30MeV (Trottet et al. 2015).Thus, the total number of accelerated ions above 30MeV( >NE 30 MeVp ) is proportional to the template normalization. Weremark that the template was generated by an ion distributionwith EC=1MeV. In order to obtain the total number of ions

Figure 2. RHESSI fitting results with low energy cutoff fixed (color coded) during the impulsive phase. First panel: corrected count rate; second panel: electron flux;third panel: spectral index; forth panel: low energy cutoff; fifth panel: power in nonthermal electrons; sixth panel: chi-squared.

4

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

( >NE Ep C) above a given cutoff EC it is then necessary to extendthe power-law ion distribution (with index 4) down to a lowerenergy cutoff (here, 2MeV) to account for the protons in theenergy range required to trigger the nuclear reactions(2–10MeV), as defined by the cross-section for such interactions(Murphy et al. 2007; Vilmer et al. 2011).

The γ-ray emission was rather weak above 2.5 MeV; wehave included the counts above this energy only to estimate anupper limit for the fitting. The results of the spectral analysisare presented in Table 2. These results average the protonnumbers and their energy for the entire duration of the event,giving a lower limit for NEp. However, it is clear that thesevalues are not constant for the entire period. Therefore, werepeated the procedure for a shorter time interval, 09:04:29 to09:04:50UT (but only fitting the spectrum below 2MeV dueto poor count statistics) in order to estimate the proton numberand energy closer to the peak of the impulsive phase of theflare. Note that the total number of ions = D>N N tE30 30 MeVpobtained from both integration times are consistent within theiruncertainties, indicating that the majority of the acceleratedions were accelerated within the 21 s window at the peak of theimpulsive phase. The results are also shown in Table 2. Weestimate the maximum flux in proton beams for the values ofEC=2, 4, 8, and 16MeV (Table 3) following a proceduresimilar to the one applied to the RHESSI spectra.

3. RADYN Modeling

The RADYN code (Carlsson & Stein 1992, 1995, 1997;Allred et al. 2015) was used to model the response of the solaratmosphere to a set of plausible heating parameters. RADYNsolves the equations of radiative hydrodynamics in onedimension with an adaptive grid and allows for direct thermalheating and/or a particle beam to be applied. The initial modelused in this work is for a plage-like atmosphere (QS.SL.HTfrom Allred et al. 2015). It assumes a 10Mm half loop with areflected top boundary and a coronal temperature of 3MK

(Vernazza et al. 1981). The transition region is placed∼1300 km above the photospheric floor, to mimic the moreactive atmospheric conditions present around sunspots. Ourmodels use the Fokker–Planck approximation and employ areturn current (Holman 2012). RADYN solves the non-LTEpopulation densities for the first six levels of the hydrogenatom, the first nine levels of the helium atom, and the first sixlevels of the calcium atom and computes the line profiles ofbound–bound and bound–free transitions within the atomicconfiguration described above. Complete frequency redistribu-tion is considered for the line transitions, which may inhibit itsability to reproduce the wings of resonance lines.We generated a grid of electron beam-driven models with

δ=3, F=3×109, 1010 and 3×1010 erg cm−2 s−1 andEC=20, 40, 60, 80, 100, and 120 keV. Proton beams of thesame flux and δ were modeled with EC=2, 4, 8, and 16MeV.Models with F=109 erg cm−2 s−1 did not show any detect-able increase in the optical continuum and their output is notpresented in this work.For the modeling of the higher order Balmer lines, we used

the non-LTE radiative transfer code RH (Uitenbroek 2001)with the latest modifications introduced by Kowalski et al.(2017). The code employs a 20 level hydrogen atom andmodels more accurately the electric pressure hydrogen linebroadening that occurs in flares. RH also uses partialredistribution, which is needed for accurate modeling of theCa II K and H line profiles. All simulations lasted 60 s with arapid onset of the beam (0.1 s) applied until t=30 s, followedby a 3 s linear decay. The remaining 27 s had no beam heatingapplied, allowing the atmosphere to relax.

4. Results

The observations described in Section 2 allowed us to obtaina set of criteria that we applied to the grids of models. Using theIS data, we obtain the constraint that the Hγ versus Ca II K lineratio should not be greater than 0.1. RHESSI and Fermiprovided energetic criteria (Tables 1 and 3), while the detectionof positive WL contrast by SDO/HMI allow us to eliminatethose models that do not show any positive WL contrast at615 nm.

4.1. Electron Beam Models

We compared the synthetic spectra from RH with theobservations. We focused our analysis on two continuummeasurements, one redwards of the Balmer jump (364.7 nm)and another close to the HMI working wavelength (615 nm) aswell as measurements of the Hγ core positions. The continuumin the vicinity of the Balmer jump remained unchanged for a

Figure 3. Fermi/GBM count spectrum in the range of 200 keV–10 MeV fromthe BGO detector, integrated between 09:04:13 and 09:05:35UT. Thespectrum was fitted with a power law (orange), 511 keV line (magenta),2.223 MeV line (green), and nuclear line template (blue), see the text fordetails. The vertical dotted lines indicate the energy range used for the spectralfitting.

Table 1Estimates of the Power of Nonthermal Electrons in the Impulsive Phase of theFlare and the Derived Maximum Flux for Given Values of the Low Energy

Cutoff with Respect to a Flaring Area in the Range of 1.1×1017 to3.3×1017 cm2

EC (keV) Power (erg s−1) Maximum Flux (erg cm−2 s−1)

20 1.6×1027 (4.85–14.5)×109

40 7.6×1026 (2.30–6.91)×109

60 5.1×1026 (1.55–4.64)×109

80 4.3×1026 (1.30–3.90)×109

100 3.8×1026 (1.15–3.45)×109

120 3.2×1026 (0.97–2.91)×109

5

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

flux equal to 3×109 erg cm−2 s−1 and EC in a range of 60 to100 keV. Higher beam fluxes resulted in an elevated con-tinuum. The continuum at 615 nm showed the same trend witha higher contrast. Table 4 and Figure 4 show that the contrast ofWL continuum peaks at greater EC values in models where theflux is greater. Broader line profiles were found for models withhigher energy flux and higher EC, while the line strengthdecreased with increasing EC. Hγ is included in the RADYNsimulation output and has good counting statistics in theobservational data set, so it was chosen as a representative forthe study of the higher order Balmer lines. The rise in the Hγwas calculated as the ratio between flare and quiescent profilesin the wavelength range of 434.159–434.186 nm. For allmodels, we investigated the temperature in the upper photo-sphere (z=300 km) and the penetration depth of the beam(Table 4). The penetration depth was defined as the range ofheights above the photospheric floor where the volumetricbeam heating reached at least 10% of its maximum. Theresponse of the Hγ/Ca II K ratio and the WL contrast areplotted in Figure 4 as a function of EC.

In order to compare our models with observations in thevisible/NUV, we combined the flare signal (Fflare) obtained att=20 s into the simulation with the nonflare signal ( ‐Fnon flare)obtained at t=0 s. Then we subtracted the nonflare signal toobtain the flare excess and divided it with the nonflare signal

=* + * - -( ) ( )‐ ‐

‐F

F ff F ff F

F

1. 1synthetic

flare non flare non flare

non flare

The electron beam-driven models with a flux of 3×109 erg cm−2 s−1 and EC between 60 and 100 keV showed apositive WL contrast at 615 nm and lie within the observedrange of energies from RHESSI. These beams produced Hγ to

Ca II K ratios of 0.122 (60 keV), 0.087 (80 keV) and 0.074(100 keV) assuming ff=0.07 (Figure 5). We found that anyemission in the higher order Balmer lines was below the noiselevels and could not be detected in the observed spectra. The60, 80, and 100 keV (F=3×109 erg cm−2 s−1) electronbeams produce very weak WL contrast of 1.02, 1.01, and1.01, respectively. Models with the same flux but lower EC,also produce emission that is too strong in the Hγ line(Figure 6). A higher energy flux (1×1010 erg cm−2 s−1 ormore) is consistent with the RHESSI constraints only forEC=20 keV (Table 1), but such a beam triggers emission thatis too strong in Hγ (Figure 6 and Table 1).

4.2. Proton Beam Models

The outputs from the RADYN/RH models of proton beamheating for a range of low energy cutoff and proton fluxes aregiven in Figure 7 and Table 5. The Hγ line of the proton beam-driven models in Figure 8 shows a similar pattern to electronbeam-driven models with more pronounced central reversal;however, in general, the line tends to be weaker for protonbeams.Of the modeled proton beams, a flux equal to 3×

109 erg cm−2 s−1 produced a positive WL contrast only forEC=2MeV, where the Hγ versus Ca II K line ratio was equalto 0.095. For a beam with a flux of 1×1010 erg cm−2 s−1

Fermi detected sufficient power if EC3.8 MeV. We do notexpect any significant differences of this beam from theEC=4MeV beam that we modeled. Table 5 and Figure 9show that for this model, the Hγ versus Ca II K line ratioreached 0.094, which is very close to the 3×109 erg cm−2 s−1

proton beam-driven model mentioned above. A flux equal to3×1010 erg cm−2 s−1 produced too strong emission in thehigher order Balmer lines (EC= 2MeV) or its energy was outof the range observed by Fermi (EC4MeV).

5. Discussion

The X1 flare event presented in this work showed anextremely hard electron spectrum (δ≈ 3), which makes itdifficult to estimate an accurate value for EC. In such a hardspectrum, the flattening of the photon spectrum below EC islikely to be the same regardless of the value of EC (seeSection 2.2). Our analysis has produced two electron and twoproton beam-driven models that can reproduce the observations

Table 2Fermi/GBM BGO Spectral Results for the Impulsive Phase

Integration Interval 09:04:13–09:05:35UT 09:04:29–09:04:50UTIntegration Time Δt 82 s 21 s

line 511 keV ∼0 (no detection) 0.023±0.026 ph s−1 cm−2 (upper limit)line 2.223 MeV 0.02±0.01 ph s−1 cm−2 0.004±0.021 ph s−1 cm−2

power-law normalization 0.011 ph s−1 cm−2 keV−1 at 300 keV 0.017 ph s−1 cm−2 keV−1 at 300 keVphoton spectral index 2.73±0.02 2.73±0.02Nuclear lines template 0.14±0.02 ph s−1 cm−2 0.51±0.09 ph s−1 cm−2

>NE 30 MeVp 1.2±0.2×1029 ions s−1 4.4±0.8×1029 ions s−1

N30 9.8±1.6×1030 ions 9.2±1.7×1030 ions

Parameters calculated from the fitting results

>PE 30 MeVp 8.3×1024 erg s−1 3.1×1025 erg s−1

>NE 2 MeVp 3.9×1032ions s−1 1.5×1033 ions s−1

>PE 2 MeVp 1.9×1027 erg s−1 7.1×1027 erg s−1

Table 3Estimates of Power in Nonthermal Protons during the Impulsive Phase of theFlare and the Derived Maximum Flux for given Values of the Low Energy

Cutoff with Respect to a Flaring Area in the Range of 1.1×1017 to3.3×1017 cm2

EC (MeV) Power (erg s−1) Maximum flux (erg cm−2 s−1)

2 7.06×1027 (21.4–64.2)×109

4 8.82×1026 (2.67–8.02)×109

8 1.10×1026 (0.33–1.00)×109

16 1.38×1025 (0.04–0.13)×109

6

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

within our observational uncertainties. Of these four models,the 1×1010 erg cm−2 s−1 and 4MeV proton beam producedthe highest WL contrast (1.06) that agrees best with theobserved value. The other three models had a lower beam fluxand showed a WL contrast of only 1.01. There was no increasedetected redward of the Balmer jump, ruling out a presence of ahot blackbody component in the photosphere and agrees withthe observations. Further examination showed that electronsdo not penetrate as deep as protons (316 versus 172 km abovethe photospheric floor), which is consistent with a lowertemperature in the upper photosphere (4614 versus 4803 K).The models also show that electron beams deliver theirenergy in the upper chromosphere (∼1150 km) for the beamswithin the energy range allowed by RHESSI, except of that

with F=3×109 erg cm−2 s−1andEC80 keV.Forprotonbeams, it is easier to penetrate through the upper chromospherewithout depositing a significant amount of energy there.We see similar observational trends for both the proton and

electron beam-driven models—the WL emission gets strongerwith increasing beam flux, but this also triggers strongeremission in the Balmer lines. With increasing EC the emissionin the Balmer lines becomes significantly weaker, while theWL emission at 615 nm shows relatively small changes (seeTables 4 and 5).The temperature profiles in Figure 10 show that the electron

beams with a flux of at least 1×1010 erg cm−2 s−1 cause a largedisturbance in the chromosphere and shift the transition region togreater geometrical heights. This is always accompanied with

Figure 4. Hγ/Ca II K ratio (black) and WL contrast (cyan) as a function of EC, and for different nonthermal electron fluxes (solid curves F=3E10, dashed curvesF=1E10, dotted curves F=3E9). The solid circles denote the values imposed by the observational constraints.

Table 4Spectral Diagnostics from Electron Beam-driven Models 20 s into the Simulation for a Range of Electron Beam Fluxes (F) and EC

EC Temperature at Penetration Rise in cont. Hγ/Ca II K Rise in Rise in cont.(keV) z=300 km (K) depth (km) >364.7 nm ratio core of Hγ 615 nm

F=3×109 erg cm−2 s−1 20 4608 480–1158 1.01 0.374 9.18 1.0240 4677 410–1156 1.01 0.307 6.53 1.0360 4630 363–1118 1.00 0.122 3.45 1.0280 4617 340–1040 1.00 0.087 2.63 1.01100 4614 316–997 1.00 0.074 2.25 1.01120 4614 293–975 0.99 0.065 2.02 1.01

F=1×1010 erg cm−2 s−1 20 4723. 433–1164 1.03 0.454 16.79 1.0740 4811 433–1156 1.04 0.414 14.36 1.1060 4990 363–1156 1.05 0.356 10.11 1.1280 4923 316–1149 1.04 0.288 7.68 1.11100 4873 293–1040 1.03 0.223 6.19 1.09120 4844 293–975 1.03 0.155 4.58 1.08

F=3×1010 erg cm−2 s−1 20 5022. 640–1167 1.11 0.433 25.54 1.2140 5336 387–1156 1.15 0.431 24.74 1.2960 5393 410–1156 1.19 0.419 22.15 1.3880 5489 340–1156 1.22 0.399 17.73 1.43100 5642 316–1156 1.23 0.367 14.39 1.44120 5571 293–1147 1.21 0.348 12.22 1.42

Note. The signal presented in each waveband is a pure flaring signal relative to the initial/quiescent state. The models that comply to observations are typed inboldface.

7

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

emission in the Balmer lines. In contrast, the proton beam-drivenmodels with the same flux leave the upper chromosphererelatively undisturbed. For both electron and proton beam-drivenmodels, a temperature rise appears deeper for higher fluxes, whilethe value of EC has only a minor effect. This supports the ideathat WLFs have a lower limit to their total flux, because onlybeams that are sufficiently intense can trigger emission in thecontinuum (615 nm, seventh column of Tables 4 and 5). This alsocontradicts the statement by Jess et al. (2008) that “there is noreason why WLF emission should not be produced in all flares.”However, the value of EC plays a significant role in the effects ofthe beam in the chromosphere. For low values of the EC, thebeam delivers its energy in the upper chromosphere where theBalmer lines are formed. We found that only those electronbeams with EC exceeding the range of modeled values(20–120 keV) dissipate the energy deep in the atmosphere andkeep the Balmer lines in absorption. Our result does not agreewith the conclusion of Fletcher et al. (2007a) that the visible/UVcontinuum requires an electron beam with a cutoff energy wellbelow 25 keV in order to deliver sufficient energy into the

atmosphere, nor with the commonly observed values of ECreported by Fletcher et al. (2007b). The power in nonthermalelectrons was 1.59×1027erg s−1 when considering EC=20 keV, which is at least an order of magnitude lower than inthe average WLF (Watanabe et al. 2017). As far as we know,there is no work presenting quantitative analysis on proton beamsin WLFs, but the deposition rate gives preference to protonbeams ( = ´> -P 7.1 10 erg sE 2 MeV 27 1p ) to be the main driver ofthe WL emission in this flare.The contribution functions of the favored electron and proton

beam-driven models are shown in Figure 11 with the mainparameters summarized in Table 6. It is defined by Carlsson &Stein (1997) as

ò c=n n t n- n ( )I S e dz, 2zz

0

1

where Iν is intensity at frequency ν, Sν is a source function, t- neis an exponential attenuation factor, and χν is the monochro-matic opacity. The beam flux appeared to be the most important

Figure 6. Detail of the Hγ line for electron beam fluxes of 3×109, 1010 and 3×1010 erg cm−2 s−1 with a filling factor of 0.07. Legend shows color coded values ofthe EC. The flaring spectra were taken 20 s into the simulations.

Figure 5. Relative flare excess for electron beam-driven models for a filling factor of 0.07. All higher order Balmer lines become weaker with increasing EC. The Ca IIK and H lines at 393.4 and 396.8 nm are also shown.

8

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

Figure 8. Detail of the Hγ line for proton beam fluxes of 3×109, 1010 and 3×1010 erg cm−2 s−1 with a filling factor of 0.07. Legend shows color coded values ofthe EC. The flaring spectra were taken 20 s into the simulations.

Table 5Spectral Diagnostics in Proton Beam-driven Models 20 s into the Simulation for a Range of Proton Beam Fluxes and EC

EC Temperature at Penetration Rise in Cont. Hγ/Ca II K Rise in Rise in Cont.(keV) z=300 km (K) Depth (km) >364.7 nm Ratio Core of Hγ 615 nm

F=3×109 erg cm−2 s−1 2000 4598 293–1078 0.99 0.095 2.45 1.014000 4621 172–907 0.99 0.063 1.77 1.008000 4659 73–753 0.98 0.046 1.31 1.0016000 4713 −46–618 0.97 0.005 1.01 0.99

F=1×1010 erg cm−2 s−1 2000 4730. 293–1093 1.01 0.167 3.85 1.054000 4803 172–907 1.00 0.094 2.53 1.068000 4907 49–753 0.99 0.079 1.86 1.0616000 5018 −46–618 0.97 0.069 1.35 1.05

F=3×1010 erg cm−2 s−1 2000 5195. 221–1149 1.09 0.429 11.59 1.224000 5292 172–929 1.10 0.116 3.70 1.258000 5440 49–753 1.10 0.103 2.54 1.2716000 5591 −53–618 1.08 0.101 1.99 1.27

Note. The signal presented in each waveband is a pure flaring signal relative to the initial/quiescent state. The models that comply with the observations are typedin bold.

Figure 7. Hγ/Ca II K ratio (black) and WL contrast (cyan) as a function of EC, and for different nonthermal proton fluxes (solid curves F = 3 × 1010 erg cm−2 s−1,

dashed curves F = 1 × 1010 erg cm−2 s−1, dotted curves F = 3 × 109 erg cm−2 s−1). The solid circles denote the values allowed by the data constraints.

9

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

factor with respect to both origin of the WL excess emissionand WL contrast. A comparison of electron beams with EC of80 and 100 keV indicates that higher values of EC result in a

deeper penetration of the beam; however, flux plays a moreimportant role. From the numerical results, it is clear that thephotospheric contribution (defined as the contribution function

Figure 10. Temperature profiles for the electron beam-driven models (panels a–c) and proton beam-driven models (panel d). The dotted line indicates the initialpreflare atmosphere.

Figure 9. Relative flare excess for proton beam-driven models. Filling factor=0.07.

10

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

integrated over heights 0–300 km) to the WL excess emissionplays a minor role in this event and the excess continuum at615 nm is predominantly formed in the lower chromosphere,no matter whether it is driven by an electron or proton beam.The simulations do not show any significant shifting of theτ=1 surface for the modeled beams. We therefore concludethat the excess WL emission is optically thin, resulting in theminor WL enhancement detected in this event.

6. Concluding Remarks

The main motivation behind this work has been to under-stand the nature of the suppressed Balmer line emissionobserved in the 2014 June 11 X1.0 white light flare. We usedparticle beam parameters constrained from RHESSI and Fermispectra to generate a number of RHD models. Our models haveshown that the spectral signatures of Type II WLF can be bestreproduced with a relatively weak particle beam that has a highlow energy cutoff (Table 6). Beams with such parameters inX-class solar flares are rare (Kuhar et al. 2016). Our modelsalso show that both electron and proton beams can beresponsible for Type II WLF, but proton beams penetratemore easily through the upper chromosphere without triggeringa strong emission in the higher order Balmer lines and at thesame time can carry more energy. The excess WL emissionthen originates over a broad range of heights in the lowerchromosphere with a relatively small contribution from thephotosphere. We found that solely based on a match betweenthe WL emission and the peak of HXR, we cannot decide if thestudied event is a Type I or Type II WLF, as Metcalf et al.(2003) did.

One of the limitations of this work is that, due to the natureof the RADYN 1D geometry, our modeling approach is moreaccurate when the line of sight does not deviate significantlyfrom the loop axis. An off-axis line of sight requires a 3D RHDmodel to account for the overlying nonflaring chromosphere.For the evaluation of the spectra, we use the relative heights offlare excess emission in Hγ and Ca II K lines. As the cores ofboth lines are formed at similar atmospheric heights, weassume that the overlying atmosphere would have similareffects to cores of both lines.Notwithstanding that Alfvén waves cannot be ruled out as

drivers of the WL emission, the present paper only focuses onelectron and proton beams as the version of RADYN used inour work does not allow us to investigate this scenario.

The research leading to these results has received fundingfrom the European Community’s Seventh Framework Pro-gramme (FP7/2007-2013) under grant agreement No. 606862(F-CHROMA). R.O.M. would like to acknowledge supportfrom NASA LWS/SDO Data Analysis grant NNX14AE07G,and the Science and Technologies Facilities Council for theaward of an Ernest Rutherford Fellowship (ST/N004981/1).P.J.A.S. acknowledges support from the University ofGlasgow’s Lord Kelvin Adam Smith Leadership Fellowship.J.C.A. acknowledges support from the Heliophysics GuestInvestigator and Supporting Research Programs.

ORCID iDs

Ondrěj Procházka https://orcid.org/0000-0003-4215-5062Aaron Reid https://orcid.org/0000-0002-7695-4834Ryan O. Milligan https://orcid.org/0000-0001-5031-1892Paulo J. A. Simões https://orcid.org/0000-0002-4819-1884Joel C. Allred https://orcid.org/0000-0003-4227-6809Mihalis Mathioudakis https://orcid.org/0000-0002-7725-6296

References

Allred, J. C., Hawley, S. L., Abbett, W. P., & Carlsson, M. 2005, ApJ, 630, 573Allred, J. C., Kowalski, A. F., & Carlsson, M. 2015, ApJ, 809, 104Boyer, R., Sotirovsky, P., Machado, M. E., & Rust, D. M. 1985, SoPh, 98, 255Canfield, R. C., Bely-Dumau, E., Brown, J. C., et al. 1986, in Energetic

Phenomena on the Sun, ed. M. Kundu & B. Woodgate, 3Carlsson, M., & Stein, R. F. 1992, ApJL, 397, L59Carlsson, M., & Stein, R. F. 1995, ApJL, 440, L29Carlsson, M., & Stein, R. F. 1997, ApJ, 481, 500Chen, P.-F., Fang, C., & Ding, M.-D. D. 2001, ChJAA, 1, 176Ding, M. D., Fang, C., & Yun, H. S. 1999, ApJ, 512, 454Fang, C., & Ding, M. D. 1995, A&AS, 110, 99Fletcher, L., Hannah, I. G., Hudson, H. S., & Metcalf, T. R. 2007a, ApJ,

656, 1187Fletcher, L., Hannah, I. G., Hudson, H. S., & Metcalf, T. R. 2007b, in ASP

Conf. Ser. 368, The Physics of Chromospheric Plasmas, ed. L. Heinzel,L. Dorotovič, & L. Rutten (San Francisco, CA: ASP), 423

Fletcher, L., & Hudson, H. S. 2008, ApJ, 675, 1645

Figure 11. Contribution functions to continuum at 615 nm of the favoredelectron (e−) and proton (p+) beam-driven models.

Table 6A Summary of the Beam Parameters That Are in Best Agreement with the Observations. For WL Emission Only the Excess is Quantified (fourth, fifth, and sixth

Columns)

Flux Ec Hγ/Ca II K WL Origin of middle 90% WL Photospheric(erg cm−2 s−1) (keV) Ratio Contrast (Height above Photosphere) Contribution

(e−) 3×109 80 9% 1% 663–1060 km 4.1%(e−) 3×109 100 8% 1% 640–1040 km 7.0%(p+) 3×109 2000 10% 1% 663–1019 km 14.2%(p+) 1×1010 4000 9% 6% 559–863 km 6.2%

11

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0003-4215-5062https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0002-7695-4834https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0001-5031-1892https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0002-4819-1884https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0003-4227-6809https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://orcid.org/0000-0002-7725-6296https://doi.org/10.1086/431751http://adsabs.harvard.edu/abs/2005ApJ...630..573Ahttps://doi.org/10.1088/0004-637X/809/1/104http://adsabs.harvard.edu/abs/2015ApJ...809..104Ahttps://doi.org/10.1007/BF00152459http://adsabs.harvard.edu/abs/1985SoPh...98..255Bhttp://adsabs.harvard.edu/abs/1986epos.conf..3.4Chttps://doi.org/10.1086/186544http://adsabs.harvard.edu/abs/1992ApJ...397L..59Chttps://doi.org/10.1086/187753http://adsabs.harvard.edu/abs/1995ApJ...440L..29Chttps://doi.org/10.1086/304043http://adsabs.harvard.edu/abs/1997ApJ...481..500Chttps://doi.org/10.1088/1009-9271/1/2/176http://adsabs.harvard.edu/abs/2001ChJAA...1..176Chttps://doi.org/10.1086/306776http://adsabs.harvard.edu/abs/1999ApJ...512..454Dhttp://adsabs.harvard.edu/abs/1995A&AS..110...99Fhttps://doi.org/10.1086/510446http://adsabs.harvard.edu/abs/2007ApJ...656.1187Fhttp://adsabs.harvard.edu/abs/2007ApJ...656.1187Fhttp://adsabs.harvard.edu/abs/2007ASPC..368..423Fhttps://doi.org/10.1086/527044http://adsabs.harvard.edu/abs/2008ApJ...675.1645F

Handy, B. N., Acton, L. W., Kankelborg, C. C., et al. 1999, SoPh, 187, 229Hao, Q., Yang, K., Cheng, X., et al. 2017, NatCo, 8, 2202Holman, G. D. 2012, ApJ, 745, 52Holman, G. D., Aschwanden, M. J., Aurass, H., et al. 2011, SSRv, 159, 107Hudson, H. S. 2016, SoPh, 291, 1273Jess, D. B., Mathioudakis, M., Crockett, P. J., & Keenan, F. P. 2008, ApJL,

688, L119Kennedy, M. B., Milligan, R. O., Allred, J. C., Mathioudakis, M., &

Keenan, F. P. 2015, A&A, 578, A72Kerr, G. S., Fletcher, L., Russell, A. J. B., & Allred, J. C. 2016, ApJ, 827, 101Kotrč, P., Procházka, O., & Heinzel, P. 2016, SoPh, 291, 779Kowalski, A. F., Allred, J. C., Uitenbroek, H., et al. 2017, ApJ, 837, 125Kuhar, M., Krucker, S., Martínez Oliveros, J. C., et al. 2016, ApJ, 816, 6Li, X. Q., Song, M. T., Hu, F. M., & Fang, C. 1997, A&A, 320, 300Lin, R. P., Dennis, B. R., Hurford, G. J., et al. 2002, SoPh, 210, 3Litvinenko, Y. E. 1999, ApJ, 515, 435Machado, M. E., Avrett, E. H., Falciani, R., et al. 1986, in The Lower

Atmosphere of Solar Flares, ed. D. F. Neidig, 483Machado, M. E., Emslie, A. G., & Avrett, E. H. 1989, SoPh, 124, 303Martínez Oliveros, J.-C., Hudson, H. S., Hurford, G. J., et al. 2012, ApJL,

753, L26Meegan, C., Lichti, G., Bhat, P. N., et al. 2009, ApJ, 702, 791

Metcalf, T. R., Alexander, D., Hudson, H. S., & Longcope, D. W. 2003, ApJ,595, 483

Murphy, R. J., Kozlovsky, B., Share, G. H., Hua, X.-M., & Lingenfelter, R. E.2007, ApJS, 168, 167

Potts, H., Hudson, H., Fletcher, L., & Diver, D. 2010, ApJ, 722, 1514Procházka, O., Milligan, R. O., Allred, J. C., et al. 2017, ApJ, 837, 46Reep, J. W., Russell, A. J. B., Tarr, L. A., & Leake, J. E. 2018, ApJ, 853,

101Scherrer, P. H., Schou, J., Bush, R. I., et al. 2012, SoPh, 275, 207Schwartz, R. A., Csillaghy, A., Tolbert, A. K., et al. 2002, SoPh, 210, 165Simnett, G. M. 1986, SoPh, 106, 165Simões, P. J. A., Kerr, G. S., Fletcher, L., et al. 2017, A&A, 605, A125Trottet, G., Raulin, J.-P., Mackinnon, A., et al. 2015, SoPh, 290, 2809Uitenbroek, H. 2001, ApJ, 557, 389Vernazza, J. E., Avrett, E. H., & Loeser, R. 1981, ApJS, 45, 635Viereck, R., Hanser, F., Wise, J., et al. 2007, Proc. SPIE, 6689, 66890KVilmer, N., MacKinnon, A. L., & Hurford, G. J. 2011, SSRv, 159, 167Švestka, Z. 1970, SoPh, 13, 471Warmuth, A., Holman, G. D., Dennis, B. R., et al. 2009, ApJ, 699, 917Watanabe, K., Kitagawa, J., & Masuda, S. 2017, arXiv:1710.09531Watanabe, K., Krucker, S., Hudson, H., et al. 2010, ApJ, 715, 651Woods, T. N., Eparvier, F. G., Hock, R., et al. 2012, SoPh, 275, 115

12

The Astrophysical Journal, 862:76 (12pp), 2018 July 20 Procházka et al.

https://doi.org/10.1023/A:1005166902804http://adsabs.harvard.edu/abs/1999SoPh..187..229Hhttps://doi.org/10.1038/s41467-017-02343-0http://adsabs.harvard.edu/abs/2017NatCo...8.2202Hhttps://doi.org/10.1088/0004-637X/745/1/52http://adsabs.harvard.edu/abs/2012ApJ...745...52Hhttps://doi.org/10.1007/s11214-010-9680-9http://adsabs.harvard.edu/abs/2011SSRv..159..107Hhttps://doi.org/10.1007/s11207-016-0904-3http://adsabs.harvard.edu/abs/2016SoPh..291.1273Hhttps://doi.org/10.1086/595588http://adsabs.harvard.edu/abs/2008ApJ...688L.119Jhttp://adsabs.harvard.edu/abs/2008ApJ...688L.119Jhttps://doi.org/10.1051/0004-6361/201425144http://adsabs.harvard.edu/abs/2015A&A...578A..72Khttps://doi.org/10.3847/0004-637X/827/2/101http://adsabs.harvard.edu/abs/2016ApJ...827..101Khttps://doi.org/10.1007/s11207-016-0860-yhttp://adsabs.harvard.edu/abs/2016SoPh..291..779Khttps://doi.org/10.3847/1538-4357/aa603ehttp://adsabs.harvard.edu/abs/2017ApJ...837..125Khttps://doi.org/10.3847/0004-637X/816/1/6http://adsabs.harvard.edu/abs/2016ApJ...816....6Khttp://adsabs.harvard.edu/abs/1997A&A...320..300Lhttps://doi.org/10.1023/A:1022428818870http://adsabs.harvard.edu/abs/2002SoPh..210....3Lhttps://doi.org/10.1086/307001http://adsabs.harvard.edu/abs/1999ApJ...515..435Lhttp://adsabs.harvard.edu/abs/1986lasf.conf..483Mhttps://doi.org/10.1007/BF00156272http://adsabs.harvard.edu/abs/1989SoPh..124..303Mhttps://doi.org/10.1088/2041-8205/753/2/L26http://adsabs.harvard.edu/abs/2012ApJ...753L..26Mhttp://adsabs.harvard.edu/abs/2012ApJ...753L..26Mhttps://doi.org/10.1088/0004-637X/702/1/791http://adsabs.harvard.edu/abs/2009ApJ...702..791Mhttps://doi.org/10.1086/377217http://adsabs.harvard.edu/abs/2003ApJ...595..483Mhttp://adsabs.harvard.edu/abs/2003ApJ...595..483Mhttps://doi.org/10.1086/509637http://adsabs.harvard.edu/abs/2007ApJS..168..167Mhttps://doi.org/10.1088/0004-637X/722/2/1514http://adsabs.harvard.edu/abs/2010ApJ...722.1514Phttps://doi.org/10.3847/1538-4357/aa5da8http://adsabs.harvard.edu/abs/2017ApJ...837...46Phttps://doi.org/10.3847/1538-4357/aaa2fehttp://adsabs.harvard.edu/abs/2018ApJ...853..101Rhttp://adsabs.harvard.edu/abs/2018ApJ...853..101Rhttps://doi.org/10.1007/s11207-011-9834-2http://adsabs.harvard.edu/abs/2012SoPh..275..207Shttps://doi.org/10.1023/A:1022444531435http://adsabs.harvard.edu/abs/2002SoPh..210..165Shttps://doi.org/10.1007/BF00161361http://adsabs.harvard.edu/abs/1986SoPh..106..165Shttps://doi.org/10.1051/0004-6361/201730856http://adsabs.harvard.edu/abs/2017A&A...605A.125Shttps://doi.org/10.1007/s11207-015-0782-0http://adsabs.harvard.edu/abs/2015SoPh..290.2809Thttps://doi.org/10.1086/321659http://adsabs.harvard.edu/abs/2001ApJ...557..389Uhttps://doi.org/10.1086/190731http://adsabs.harvard.edu/abs/1981ApJS...45..635Vhttps://doi.org/10.1117/12.734886http://adsabs.harvard.edu/abs/2007SPIE.6689E..0KVhttps://doi.org/10.1007/s11214-010-9728-xhttp://adsabs.harvard.edu/abs/2011SSRv..159..167Vhttps://doi.org/10.1007/BF00153567http://adsabs.harvard.edu/abs/1970SoPh...13..471Shttps://doi.org/10.1088/0004-637X/699/1/917http://adsabs.harvard.edu/abs/2009ApJ...699..917Whttp://arxiv.org/abs/1710.09531https://doi.org/10.1088/0004-637X/715/1/651http://adsabs.harvard.edu/abs/2010ApJ...715..651Whttps://doi.org/10.1007/s11207-009-9487-6http://adsabs.harvard.edu/abs/2012SoPh..275..115W

1. Introduction2. The X1 Flare on 2014 June 11: Observations and Data Analysis2.1. White Light from SDO/HMI Observations2.2. Hard X-Rays from RHESSI Observations2.3. Gamma-Rays from Fermi/GBM Observations

3. RADYN Modeling4. Results4.1. Electron Beam Models4.2. Proton Beam Models

5. Discussion6. Concluding RemarksReferences